Thread: monotonic or not?

my teacher was explaining to determine if

4-(1/n) is monotonic you do the following....


(1/n) ? (1/n+1)

(n) ? (n+1)

(n) < (n+1)

0 < 1

ok....so i have this...what does this tell me?
1. what tells me this is monotonic?
2. what tells me this is bounded?

First you have to know what n is. n basically is a "natural" number, meaning from 1,2,3,4...

Now, when n=1, you have 1/n = 1/1 = 1
when n=2, you have 1/2
when n=3, you have 1/3, and so on...

What do you notice? You should that 1/n gets smaller as n gets bigger right?

Now, what does do for 4-1/n? As n gets bigger, what would happen to 4-1/n?

What your teacher is trying do is to get you to understand the relationship between 1/n and 1/(n+1), well, think about it, which one should bigger? That would tie in with above.

Now, monotonic sequence is basically a sequence such that it always decrease, increase, or remain constant as n gets bigger, so what do you think 4-1/n is?

Now, bounded simply implies that a sequence is "bounded" by a certain value, like 1/n itself will decrease, but it will never get as low as 0, in other words, 0 is greater than or equal to 1/n